We all have personal biases. How can a person know if his choice not to listen to the decision of a gadol is not simply based on some bias? Once you establish that the words of a gadol are not truly binding, what worth are the words of a gadol at all? Essentially, it seems to me that they have become (again, for all intents and purposes) meaningless.
I think bias can be overcome, but not always. Jak's example about judges recusing themselves is right on point. Judicial ethics require a judge to recuse himself when he has a personal stake in the case. Surely a judge who is the majority owner of a corporation that is in court should recuse himself. But the canons of ethics do not require a judge who owns a few shares or a judge whose son happens to go to the school that is being sued to recuse himself. That's because bias is everywhere but we assume that bias can be overcome in some cases, but not others.
However, if the decision really has grave spiritual impact (schooling, shuls, etc.), and a person simply cannot decide which house to purchase because he is having difficulty balancing the various spiritual factors, and a rav says that clearly one is superior, I cannot fathom why he shouldn't heed that advice (unless perhaps the question changes, i.e. a new element comes into play.)
Perhaps you ask questions about every subject under the sun. Which tomato do I purchase - the Roma, or the vine? If so, then I can see why you don't feel an obligation to listen. But I only ask questions to which I truly do not know the answer. Therefore, regardless of the true status of such advice, it seems to me obvious that it should be personally binding.
Jak's suggestion about making a Rav's advice binding is far from the only solution and probably not the best. If a person is truly worried that his biases are influencing his decisions, he could consider his wife's views binding. If the sole problem is that biases blind and other people who do not share the same bias are more objective, then why ask a Rav at all? Why not get a therapist or someone else trained to deal with identifying biases in people? We can solve the bias problem by appointing anyone as an authority.
So why choose a Rav? The answer must be because the Rav is more likely than other people in question to get the answer to the question correct. As Joseph Raz would say, we accept an authority because he is more likely to determine what right reason demands than the subject. In some cases a Rav is clearly most competent in figuring out the answer. Since Rabbanim tend to specialize in Halacha, his opinion should be granted great weight. But I'd demur against making his authority preemptive, because no one but the questioner is ever completely capable of understanding his situation as well as the person himself. Language and other factors are a barrier to transmitting information efficiently, so it becomes impossible for the Rav to fully comprehend the issue at hand in its entirety. People, even biased people, should be willing to evaluate the answer and weigh it against other factors.
This is an epistemological problem and one not easily solved. From a practical perspective, I'd suggest a person accept a Rav's psak unless he feels the psak is completely wrong. In that case, he should follow the procedures laid down in Halacha and ask another Posek of "greater" stature and inform him of the earlier Posek's ruling. So basically when it comes to personal psak for a single individual we don't disagree in practice, only in theory.
The difference is when it comes to global pronouncements or advice not of the Halachic nature. Let's focus on the latter issue, because I'd rather not get into the whole Askanim problem that Harry properly brings up. When the issue is not Halachic, it is less plausible that the Rav is more likely to come to the correct conclusion than the person asking the question. So the Rav's opinion should be given less weight. What about bias? It's a problem. But at this point it becomes a question of weighing factors. The Rav might be more objective, but he is less qualified to answer the question. So the individual has to make the decision for himself. If it's an important issue he seek advice from a number of sources, preferably from people who are aware of the problem, but also from people who are detached. I believe different perspectives will illuminate the underlying problems and expose biases.
Not considering a ruling or opinion binding does not render it meaningless, even practically. Imagine someone goes to a doctor and is told he has a fatal illness and only treatment A will save his life. Further imagine that treatment A is risky. Now, most people respect their doctor's medical advice and don't frequently reject the advice out of hand. But in such a case, most people would look for a second opinion. Why? Because doctors, like other experts, might be wrong.
Jak is essentially arguing that advice is meaningless because people will decide what they want to do with or without the advice. But that just isn't true. The patient will speak to other doctors, do his own research, etc. But his decision will be at least partly based on how much he respects the first doctor, and the odds that the doctor is right. I believe that if the person had spent months researching the issue and never spoken to the doctor, he might have come to a different conclusion or at the very least would reach that conclusion differently.